system as a whole. More precisely, a is the acceleration of the centre of mass of the system about which we shall study in detail in Chapter . Any internal forces in the system are not to be included in F . Fig.
. Acceleration at an instant is determined by the force at that instant. The moment after a stone is dropped out of an accelerated train, it has no horizontal acceleration or force, if air resistance is neglected. The stone carries no memory of its acceleration with the train a moment ago.
. The second law of motion is a local relation which means that force F at a point in space (location of the particle) at a certain instant of time is related to a at that point at that instant. Acceleration here and now is determined by the force here and now, not by any history of the motion of the particle (See Fig. .
) . Example . A bullet of mass . kg moving with a speed of m s – enters a heavy wooden block and is stopped after a distance of cm.
What is the average resistive force exerted by the block on the bullet? Answer The retardation ‘ a ’ of the bullet (assumed constant) is given by – u a – m s – m s . − − × × The retarding force, by the second law of motion, is = . kg × m s - = N The actual resistive force, and therefore, retardation of the bullet may not be uniform.
The answer therefore, only indicates the average resistive force. ⊳ Example . The motion of a particle of mass m is described by y = + ut gt . Find the force acting on the particle.
Answer We know ut gt + Now, v u gt + acceleration, v a g Then the force is given by Eq. ( . ) F = ma = mg Thus the given equation describes the motion of a particle under acceleration due to